Two dice are rolled simultaneously. Find the probability of each of the following events :(1) Event A : the sum of the numbers on the upper faces is 7.(2) Event B : the sum of the numbers on the upper faces is a multiple of 5.(3) Event C : both dice…

Answer: \(P(A) = \dfrac{1}{6}\), \(P(B) = \dfrac{7}{36}\), \(P(C) = \dfrac{1}{6}\)

Each die shows 1 to 6, so \(n(S) = 6 \times 6 = 36\).

(1) A = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}, \(n(A) = 6\), \(P(A) = \dfrac{6}{36} = \dfrac{1}{6}\).

(2) Possible sums that are multiples of 5 are 5 and 10.
B = {(1, 4), (2, 3), (3, 2), (4, 1), (4, 6), (5, 5), (6, 4)}, \(n(B) = 7\), \(P(B) = \dfrac{7}{36}\).

(3) C = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}, \(n(C) = 6\), \(P(C) = \dfrac{6}{36} = \dfrac{1}{6}\).